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According to http://en.wikibooks.org/wiki/Automobile_Repair/Honda/Odyssey/Change_engine_oil_and_filter, you need 5 quarts of oil.
4
4.6 Quarts including the filter - Assuming a 2004 HONDA ODYSSEY with 3.5L 6-cyl Engine Code J35A4
How many Axles does Honda Odyssey have?
For an oil/filter change it holds 4.25 liters or 4.5 quarts.
The 2010 Honda Odyssey has 24 valves.
The 2012 Honda Odyssey has 24 valves.
The 2002 Honda Odyssey has 24 valves.
The 2007 Honda Odyssey has 24 valves.
The 2014 Honda Odyssey has 24 valves.
The 2009 Honda Odyssey has 24 valves.
The 2006 Honda Odyssey has 24 valves.